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      An effective model to decompose linear programs for parallel solution

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      Author(s)
      Pınar, Ali
      Aykanat, Cevdet
      Date
      1996-08
      Source Title
      Applied Parallel Computing Industrial Computation and Optimization Third International Workshop, PARA '96
      Print ISSN
      0302-9743
      Publisher
      Springer
      Pages
      592 - 601
      Language
      English
      Type
      Conference Paper
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      Abstract
      Although inherent parallelism in the solution of block angulax Linear Programming (LP) problems has been exploited in many research works, the literature that addresses decomposing constraint matrices into block angular form for parallel solution is very rare and recent. We have previously proposed hypergraph models, which reduced the problem to the hypergraph partitioning problem. However, the quality of the results reported were limited due to the hypergraph partitioning tools we have used. Very recently, multilevel graph partitioning heuristics have been proposed leading to very successful graph partitioning tools; Chaco and Metis. In this paper, we propose an effective graph model to decompose matrices into block angular form, which reduces the problem to the well-known graph partitioning by vertex separator problem. We have experimented the validity of our proposed model with various LP problems selected from NETLIB and other sources. The results are very attractive both in terms of solution quality and running times. © Springer-Verlag Berlin Heidelberg 1996.
      Keywords
      Linear programming
      Matrix algebra
      Optimization
      Graph partitioning
      Graph partitioning by vertex separators
      Hypergraph model
      Hypergraph partitioning
      Inherent parallelism
      Multilevel graph partitioning
      Parallel solutions
      Solution quality
      Graph theory
      Permalink
      http://hdl.handle.net/11693/27748
      Published Version (Please cite this version)
      https://doi.org/10.1007/3-540-62095-8_64
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      • Department of Computer Engineering 1435
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